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人気のある微分積分 >

derivative f(x)= 1/(6sqrt(x^3))

解

導関数

f (x) = \frac{1}{6 x ^{3}}

解

- \frac{x ^{2}}{4 ( x ^{3} ) ^{\frac{3}{2}}}

解答ステップ

\frac{d}{d x} (\frac{1}{6 x ^{3}})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{6} \frac{d}{d x} (\frac{1}{x ^{3}})

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

= \frac{1}{6} \frac{d}{d x} ((x^{3})^{- \frac{1}{2}})

連鎖法則を適用:

- \frac{1}{2 ( x ^{3} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{3})

= - \frac{1}{2 ( x ^{3} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

= \frac{1}{6} (- \frac{1}{2 ( x ^{3} ) ^{\frac{3}{2}}} \cdot 3 x^{2})

簡素化

\frac{1}{6} (- \frac{1}{2 ( x ^{3} ) ^{\frac{3}{2}}} \cdot 3 x^{2}) : - \frac{x ^{2}}{4 ( x ^{3} ) ^{\frac{3}{2}}}

= - \frac{x ^{2}}{4 ( x ^{3} ) ^{\frac{3}{2}}}

グラフ

人気の例

tangent f(x)= 2/(x-6),\at x=8

t an g e n t f (x) = \frac{2}{x - 6}, at x = 8

integral from 2 to 5 of x/(x^2+4x+20)

\int_{2}^{5} \frac{x}{x ^{2} + 4 x + 20} d x

derivative (x^2-16x+64)(x^2+64x+4)

d er i v a t i v e (x^{2} - 16 x + 64) (x^{2} + 64 x + 4)

integral of (sec(1/x))/(x^2)

\int \frac{sec ( \frac{1}{x} )}{x ^{2}} d x

(dy}{dx}=(\frac{x-y)/x)

\frac{d y}{d x} = (\frac{x - y}{x})